Degeneration of K\"{a}hler-Einstein Manifolds II: The Toroidal Case
Differential Geometry
2007-05-23 v4
Abstract
In this paper we prove that the K\"{a}hler-Einstein metrics for a toroidal canonical degeneration family of K\"{a}hler manifolds with ample canonical bundles Gromov-Hausdorff converge to the complete K\"{a}hler-Einstein metric on the smooth part of the central fiber when the base locus of the degeneration family is empty. We also prove the incompleteness of the Weil-Peterson metric in this case.
Cite
@article{arxiv.math/0303113,
title = {Degeneration of K\"{a}hler-Einstein Manifolds II: The Toroidal Case},
author = {Wei-Dong Ruan},
journal= {arXiv preprint arXiv:math/0303113},
year = {2007}
}
Comments
The assumption of simple in the toroidal degeneration is removed using base extension